Suppose LaCie Disk B is already a proper backup of LaCie Disk A
rsync -aE /Volumes/LaCie\ Disk\ A/ /Volumes/LaCie\ Disk\ B
No files will be copied since B is already the same as A, but any files with resource forks will now have their last-modified times changed to the current time on the destination disk.
Now running the same command again will cause rsync to recopy those files due to the differing last-modified times. This will cause the last-modified times to revert to what they were before.
The result is that every other time you run the command, any files with resource forks will be recopied, even though they haven't changed.
I noticed this because I have some 50GB files with resource forks that never change (raw video files).
The filesystems on both drives read as "Mac OS Extended". The filesystem for the computer reads as "Mac OS Extended (Journaled)". The OS is Mac OS X 10.5.2

Sorry you are right. The problem is with Apple's rsync.
I thought that make install would overwrite Apple's rsync with the new one. I even checked with rsync -h, but I must have seen the directory name and thought it was the version number.